I can't top the third post here, and I'm guessing no one can...but I think of Jaoquim Phoenix as one answer here. He was an actor who discovered that it was possible for him to become a musician. This revelation of possibility seems similar to Gatsby's realization that he really could go out and get what he wanted from the world.
There are many examples of people in a position of celebrity, and those who have risen to fame on the power of a particular cause, who have been discovered to have secrets which completely contradict the public image associated with them.
Anyone who thinks that his or her money (especially "new" money) will bring them happiness or influence could be a modern-day Jay Gatsby. The above post mentions a couple of musicisns, but I think there are lots of Hollywood types who could fall into this category. Why is Angelina Jolie a U.N. goodwill ambassador? Why does Bono preach about how soceity should behave? Oprah Winfrey? I would never discount the good that these people have done for others, but it also strikes me as self-serving.
There was an EXCELLENT hour on NPR a few weeks ago discussing this very topic. One of the scholars argued that modern rappers, like Jay-Z and Diddy are much like Gatsby.
Here is the link to the podcast. You should check it out!
A modern-day Jay would have Jay's character traits. You need to find someone who will commit the acts Jay would.
Imagine these characteristics for choosing your current day character:
1. APPEARS DIFFERENT ON THE OUTSIDE FROM HIS REALITY INSIDE: Jay gives every idea that he is a gentleman. But, regularly Nick catches him in lies. His dealings with "Chicago" and "Detroit" when the phone rings suggest that he has something to do with the boot-legging industry of the era, an illegal act. His connections to Meyer Wolfsheim further support this premise.
2. WILL STOOP TO ANY LEVEL TO GET WHAT HE WANTS: Jay wants Daisy. He spends five years of intense commitment to developing a lifestyle that would be worthy of her. Then, he will stop at nothing, not destroying marriages or commiting murder, to get what he wants.
To me, this sounds like a stereotypical politician, or even a highly successful CEO who has protected his interests. I would suggest looking at some of these who have been in the spotlight for a wrongdoing and then they claim their innocence burying a problem.